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Home » + 24x + 18x + 4x² = 180 - Baxtercollege

+ 24x + 18x + 4x² = 180 - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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\( 16^4 = (-1)^4 = 1 \), but \( 16 \equiv -1 \), excluded
So solutions to \( x^4 \equiv 1 \pmod{17} \) are \( x \equiv 4, 13, 13...
Wait: \( 4^4 = 256 \equiv 1 \), \( 13^4 = 28561 \), but earlier comput...
But \( 4, 13 \), and since group is cyclic, primitive roots â actual...
But we need order 4. \( 4^2 = 16 \equiv -1
e 1 \), so order 4. \( 13^2 = -1 \), \( 13^4 = 1 \), so both have orde...
Now check: \( 4
ot\equiv \pm1 \), \( 13 \equiv -4 \), so also not \( \pm1 \). So both...
Wait, earlier list missed: \( (-4)^2 = -1 \), so \( (-4)^4 = 1 \), \(...
But is there another? Try \( x = 2 \): \( 2^4 = 16

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